Go to Crescent Island and meet Cid and Mid between both points of the crescent, then you should be back on track.

Yes it is a bit vague, but it seems to be enough detail for an answer without giving away any plot spoilers and I did my best to not give anything away, even though the game is almost as old as me.Interesting point, the game is over 10 years old so they shouldn't really be classed as spoilers anymore, shouldn't they?

If you've fought the Clay Claw yet, you have to go back into the ruins (the metal pad near Crescent Town) Cid and Mid will send you to get Adamantite. To get this, you have to go back to the Tycoon Meteor.